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Category Archives: recursion
Post without words #3
(This is my 200th post! =)
Posted in counting, pattern, pictures, posts without words, recursion
11 Comments
The hyperbinary sequence and the CalkinWilf tree
And now, the amazing conclusion to this series of posts on Neil Calkin and Herbert Wilf’s paper, Recounting the Rationals, and the answers to all the questions about the hyperbinary sequence. Hold on to your hats! The CalkinWilf Tree First, … Continue reading
Posted in arithmetic, computation, induction, iteration, number theory, pattern, proof, recursion, sequences, solutions
Tagged algorithm, binary, CalkinWilf, Euclidean, Haskell, hyperbinary, tree
6 Comments
More hyperbinary fun
When I originally posed Challenge #12, a certain Dave posted a series of comments with some explorations and partial solutions to part II (the hyperbinary sequence). Although I gave the “solution” in my last post, no solution to any problem … Continue reading
Posted in challenges, induction, pattern, proof, recursion, sequences, solutions
Tagged hyperbinary, induction
12 Comments
Challenge #12 solution, part III
And now for the solution to problem #3 from Challenge #12, which asked: how many ways are there to write a positive integer n as a sum of powers of two, with no restrictions on how many powers of two … Continue reading
Recounting the Rationals, part III
First, a quick recap: continuing an exposition of the paper Recounting the Rationals, we’re investigating the tree of fractions shown below (known as the CalkinWilf tree), which is constructed by placing 1/1 at the root node, and giving each node … Continue reading
Posted in number theory, pattern, proof, recursion
10 Comments
Recounting the Rationals, part II (fractions grow on trees!)
Today I’d like to continue my exposition of the paper “Recounting the Rationals”, which I introduced in a previous post. Recall that our goal is to come up with a “nice” list of the positive rational numbers — where by … Continue reading
Posted in infinity, number theory, pattern, recursion, sequences
22 Comments